Quantitative spectral analysis



N 1934- o. s. DUFFENDACK ET AL 1,979,964

QUANTITATIVE SPECTRAL ANALYSIS Filed March 14, 1932 4 Sheets-Sheet 2 I! IN III! III 38 014511111 zzzdack M24172: 01%! e.

Nov. 6, 1934. o. s. DUFFENDACK ET AL 1,979,964

QUANTITATIVE SPECTRAL ANALYSIS Filed March 14/ 1932 4 Sheets-Sheet 3'- m w m & .zm.rzou 2352i RELATIVE INTENSITY L06 IB Nov. 6, 1934- o. s. DUFFENDACK ET AL 1,979,954

QUANTITATIVE SPECTRAL ANALYSIS Filed March 14, 1952 4 Sheets-Sheet 4 ARC CURRENT AMP'ERES awe/Wm My, W?

Patented Nov. 6, 1934 UNITED STATES 1,979,964 I QUANTITATIVE SPECTRAL ANALYSIS on s. Dufl'endack and Ralph A. Wolfe, Ann

Arbor, Mich.

. Application March 14, 1932, Serial No. 598,791

11. Claims.

In'the making of alloys and other mixtures and compounds of materials, it is often highly desirable to know very promptly what is the amount of a given constituent in the melt so that if there is too much of it, heating or other treatment can be carried further until more of the element has been removedfor if there is too little of it, the treatment may be brought to an end to conserve the amount remaining or more of a needed constituent may be added to the melt. The only practical method of quantitative analysis now available is chemical analysis and chemical analysis of many compounds and alloys takes a number of hours or even a number of days as, for example, when repeated filtering is necessary. Before this can be accomplished, it may have been necessary to discontinue the'treatment for other reasons, and in the case of an alloy, pour the melt. The resulting a oy or mixture will lack the desired compositi of elements because of lack of accurate contro of the treatment, and

this in turn is due to lack of knowledge of the r analysis of the material during the critical stage of treatment.

There are also certain substances that are very dimcult to analyze chemically; For example, it is almost impossible to separate nickel and co- .balt or nickel and iron by chemical means. For certain other substances no satisfactory quantitative chemical analysis has been developed.

This invention has to do with a method of quantitative analysis by study of the spectrum of the material. In the case of certain alloys with which the method has been used by employing suitable equipment hereinafter described, an accurate analysis may be made in 15 or 20 minutes compared with several days required for chemical analysis. Our method of spectroscopic analysis can also be successfully employed in the case of substances such as those above referred to which can only be analyzed with difiiculty, if at all, by chemical methods.

While our method is of general applicability it cannot be employed for the estimation of such elements as chlorine, bromine, iodine, nitrogen and oxygen which will usually not reveal themselves in the are or spark from which the spectrum is obtained. There are, however, some bands in the spectra ofthe compounds of these elements which can be made to appear under certain conditions. It is essential to a complete understanding 0 the invention that the limitations of prior methods of spectral analysis be clearly understQQd. Hence the following discussion.

Perhaps the first serious attempt at quantitative analysis was made by Lockyear who in 1874 found that, when electric arcs or sparks were maintained between metallic electrodes, the distances from the electrodes at which lines of elements in the metals could be detected varied with the amounts of the elements in the electrodes. In other words, the lengths (linear) of the spectral lines are sensitive to the amounts of the elements producing them. When the quantity of an element in the electrode is diminished, the lengths of its spectral lines decrease until finally all but a few longest disappear. Unfortunately the length of the lines is also afiected seriously by other factors such as the amount of the electric current, the width of the gap, the nature and pressure of the gas in which the arc, or spark was situated and other experimental conditions so that no satisfactory method of analysis based on the lengths of the spectral lines has been devised.

In 1882 Hartley attempted to determine the amount of beryllium present in certain compounds of cerium and plainly had conceived the possibility of quantitative analysis from a determination of the amount of a certain substance that must be present in a mixture for it to reveal its presence by its spectral lines. He preferred to work with solutions and showed that the spectra of metals in solution were identical with their spectra in solids. Sparks between graphite electrodes saturated with a solution of a metal were found to give persistent lines which could be correlated with the percentage of the element in the solution. Certain elements give lines which persist until the dilution is of the order of 99%.

while others could be detected when present in minute traces-one part in 10,000,000,000 in the case magnesium. The sensitivity could be greatly increased by using stronger sparks. This method of persistent lines was extended by Pollock and Leonard who were able to get quantitative results in certain cases. They classified a large number of lines of a number of elements according to the following scheme:

(tau) =lines seen with the metal, but not in strong solutions.

(sigma) =1ines seen with strong solutions, but not with 1% solutions.

(phi)=lines seen with 1% solutions, but not with .1% solutions.

(xi) =lines seen with .1% solutions, but not with .01% solutions.

(psi) =lines seen with .01% solutions, but not with. $101.70 solutionsa ley and of Pollock and Leonard come from two )sources. Ordinary electric sparks are feeble sources of light and are at best capricious and diiiicult to control. They are apt to strike first at one point and then at another on the electrodesand when they do so often exhibit quite wide differences in character. Furthermore the .detection of a spectral line depends quite as much on the spectrograph, exposure, plate emulsion, and plate development as it does upon the concentration of solution and some of these factors are practically impossible to maintain constant. For example, it is extremely diflicult to photograph a spectrum on two diil'erent plates and get \identical results.

Some'of the difficulties in the method of per lsistent lines were overcome by de Gramont. Beginning in 1895-, de Gramont worked almost continuously until his death on the problem of quantitative spectral analysis and succeeded in devising methods which seem definitely possible of development into practicable ones. Certainly much of the ground work for a successful method has been laid. De Gramont's first advance over the older methods came in the introduction of electrical condensers into his spark circuit. A condensed spark was found to bring out not only the lines of elements occurring as metals in the electrodes but also the lines of elements occurring as halides or other compounds. Some non-metallic elements, particularly metalloids, also revealed their presence in the condensed sparks of 'de Gramont. When self inductance as well as capacitance is added to the circuit, the possibilities of varying the nature of the spark are greatly increased. By manipulating the capacitance and inductance of the spark "circuit progressive and significant changes in the spectrum of the" spark are produced which changes can be correlated with the amounts of different elements present in the electrodes.

De Gramont investigated the condensed spark spectra of minerals, and alloy mixtures containing varying concentrations of a particular element, and found that the lines of this element progressively vanish as the concentration decreases.

The last lines to disappear were called by de- Gramont the "raies ultimes", a name that has come into common use among spectroscopists.

- The "raies ultimes are usually found to coincide with the long lines of Lockyear and the "persistent lines" of Hartley. It was Hartley who first noticed that these lines are not always the strongest lines in the spectrum of an element. They are, however, usually found to be the first lines of strong series in the are or the spark spectrum of the element.

The question of when a line disappears from the spectrum of a spark is one diflicult to settle because it depends on such factors as plate sensitivity, exposure, and development and on the characteristics of the spark '(or arc) as well as on the concentration of an element in the electrodes.

Consequently it is not surprising to find that efforts were made to determine results from the strength of a spectral line rather than from their.

' or alloys of known concentrations. By comparison and interpolation one decides that the concentration in the unknown lies between those of two of the standards and thus makes an analysis within these limits. This methodrequires the photographing on the same plat'e of the spectra of the unknown and of a series of standards. The exposures must necessarily be equally long, the spark or are circuits in all cases be identical in characteristics as to voltage, current. inductance and capacitance, and the sparks must be equally well focussed on the slit of the spectrograph. Unfortunately those who have worked with electric sparks and arcs and lenses and spectographs know that it is impossible to reproduce every condition of one exposure in another; they are not equivalent, and so the method is subject to considerable uncertainty and error.

The second method of analysis is based upon the strengths of selected spectral lines of the element under analysis relative to their strengths in standard alloys. The relative strengths of the selected spectral lines canbe determined in various ways. One method is to measure their densities by means of'a microphotometer or densitometer. The methods for doing this are well known and need no description here. Another method consists in producing spectral lines of varying the lines lies in the fact that the lines do not end abruptly but gradually vanish so that the length of the line is a somewhat indefinite quantity. While the methods described above based fundamentally upon the work of Lockyear, Hartley'and de Gramont have attained a considerable measure of success, they have invariably its been found difilcult to apply and more or less 180 unreliable. They require a technique of very high order because of the large errors that can be introduced by slight deviations in the conditions of the apparatus. I

Furthermore it is the opinion of applicants, reached after considerable sad experience, that any method based upon a comparison of the strengths of spectral lines as recorded on. a photographic plate is necessarily unreliable.

It is a reasonable assumption that the intensity of a spectral line in an are or a spark is proportional to the concentration in the vapor of the arc of the element producing the line. But the blackness or strength of the line on the photo graphic plate varies in a complicated way with the intensity of the line in' the source. The relationship is shown graphicallvin Figure l in which the blackness of the line on the metals plotted against the log of the intensity of the set v 1,979,984 line in the source. It will readily be observed that for' a constant ratio of blackening,

a I II 3 27 one may have a great difference in the ratio of the concentration of an element in a material.

One must determine the relative intensities of lines in the source in order to determine the concentration of an element. Methods for measuring such relative intensities have been devised and will now be discussed.

The work of Gerlach andSch'sei'tzer deserves careful consideration for they have developed a method of spectroscopic analysis that has proved to be practicable and useful though the accuracy attained by their methods (a maximum error of 20 per cent) is not great enough to satisfy the demands of modem industry. However, these men. attacked the gross uncertainties of the previous methods/and eliminated them and paved the way for the more accurate analysis that is possible today.

Perhaps the greatest errors in theolder methods of analysis came from the comparison of lines in different spectrograms. As pointed out above, it is, practicallyimpossible to make equivalent exposures for the recording of spectra. Realizing this, Gerlach developed a method of internal control in which the analysis was based upon the relative strengths (opacities) of selected lines of the element under test and of another, the principal or basic, element in the present in varying amounts, that is, 1 per cent,

0.1 per cent,.0.01 per cent, etc., and finds in the spectrogram of each sample a pair of lines, one of the test element and one oi the'basic element, of equal strength. These pairs of lines are ex= amined in the spectrum of the unknown, and by comparison with theirrelative strengths in the prepared series, analysis is made. If none of the pairs have equal strength in the spectrum of the unknown, an estimate of the concentration of the test element is made by an interpolation between the steps in the standard series.

In 1927 Schweitzer showed that the relative strength of a pair of lines (Pb in Sn) may vary considerably'with the conditions of excitation.

Using a spark source, he showed that the relative strength of a pair of lines may be greatly altered by varying the capacitance or the inductance in the circuit or by changing transformers or by varying the primary current of the transformer. However, he found a few pairs of lines, which he called homologous lines, whose relativestrengths changed but little with the variations in the discharge conditions. He tested various pairs of lines over wide limits of variation of capacitance, inductance, etc., and found their homologous pairs. His method, like Gerlachs,

consisted in determining the percentage compo-. sition of an alloy for which particular homolcgous pairs had equal strengths. The analysis of an unknown was then made by determining spectrum must be twelvetimes as long as for which of the selected pairs had equal strength. As in Gerlachs method, the analysis was exact only if a selected pair had equal strength. Otherwise good judgment must be exercised in interpolating between percentages for which different M v pairs were equally strong. This method is known as the "absolute Schweitzer.

Schweitzer alsoimproved the method of analysis by fixing the excitation conditions. He selectmethod of Gerlach and ed a pair of lines of the basic element of the alloy being analyzed, one a spark line and one an arc line, and found the conditions (amount of capacity, inductance, etc.) under which these lines are equally strong. Then he kept the discharge circuit constantand used for his analysis only those spectrograms in which this pair of lines were of equal strength. He assumed that when these lines were equally strong the excitation of the vapor of the alloy was always the same. 9:

At the same time, Schweitzer extended the absolute method by making use of the spectrum of an auxiliary element. It sometimes happens that for a certain alloy very few homologous pairs of lines can be found, In such a case, Schweitzer superposes on the spectrum 01 the alloy the spectrum of an auxiliary element. The lengths of time of exposure oi the alloy and of the auxiliary element are intuch ratio as to make a selected pair of lines, one of the basic element of the alloy and one of the auxiliary element, have equal strengths. Standardizing the exposure ratio in this way and the discharge circuits as before, he now finds the percentage compositions of the alloy for which homologous pairs of lines, one of the test elements and one of the auxiliary element, have equal strength.

A concrete example will help to make Schweitzers method clear. In the determination of the percentage of bismuth in lead, it was found 11 that very few homologous pairs of Bi and Pb lines are available and so Sn is used as an aumTliary element. The procedure is as follows:

I. To reproduce discharge conditions, A 3352 and A 3331 of Sn must be equally strong. The 2.20 first is a spark line and the second an arc line oi tin. They have equal strength when the capacie tance in the discharge circuit-is 6000 cm.

H. To determine the exposure time ratio of the alloy and the tin A2422 of Sn and A 2412 of Pb 1.4: must be equally strong. These lines have equal strength for a ratio of exposure times of alloy and tin equal to 12; that is, the exposure for the alloy the tin spectrum. I

HI. Using the above discharge conditions and exposure ratios, a series of Bi-Pb alloys with varying Bi content gives a set of homologous pairs of Bi and Sn'lines that have equal strengths for the following percentage compositions of Bi in 135 the Bi-Pb alloys.

Percent Bl in Bi-Pb Homologous lines alloy for equal lino strengths Percent Bi 2938 or 2898 Sn 3009"; 6 Bi 2731 Sn 2765 3 Bi 3068 Sn am a Bi 2938 or 2898 Sn 2851 1.5 5 Bi 3068 En 3009 l Bi 30% Sn 3142 0. 6 Bi 2938 Sn 0. 5 Bi 2938 Su 2765 0. 1 Bi 3068 Sn i142 0. 015 Bi 3068 Sn 321 0.004 1" The line strengths were ordinarily estimated by mere eye examination, although the use of some form microphotometer or densitometer was suggested by Schweitzer. Later a further broad- 5 ening of the method by introducing a substituted auxiliary spectrum was developed. This method does not difler in principle from the other methods described and needs no exposition here.

This absolute" method of Gerlach and Schweitzer is subject to criticism on two points in particular. In the first place it is obvious that exact analyses can be made only it the percentage composition of the alloy happens to be one of those for which a "homologous pair of lines have equal strength. No good scheme for interpolating between these discrete percentages is obvious, and a considerable error may result from a necessary interpolation.

One scheme for interpolating between fixed percentages and even for making provisional analyses, consists in determining the change in strength of a spectral line with a' change in the concentration of an element in an alloy. How-- ever, it seems that improvement in interpolating between the percentages fixed by homologous pairs is desirable.

Another weakness in the methods oi. Gerlach and Schweitzer lies in their dependence upon equal strengths of homologous pairs and control lines. As stated earlier, it seems more logical to consider relative intensities of spectral lines in the source than relative strengths of lines in the photographic plate. Although the use only 01' lines of equal strength reduces errorsdue to the comparison of opacities rather than intensities, one must contend continually with percentages between those fixed by homologous pairs and give consideration to relative opacities and relative intensities.

Recognizing the two weaknesses of the absolute method described in the foregoing parae.

graphs, Scheibe and Neuhiiussermade attempts to improve and refine the method. This, they did by using a rotatingdisk sectored in the .form

spectrograph. One form of such a disk is shown in Figure 11. The rotating sectored. disk efiected a logarithmic variation in the time of exposure along the length of the slit. Since the blackening of a photographic plate is proportional, over a given range, to the logarithm of the intensity of light falling upon it, it will, with a constant intensity source, be proportional to the logarithm of the time of exposure. Therefore, over a cersuch a sectored disk is employed, will be proportional to the logarithm of the intensity of the line in the source. Scheibe and Neuhiiusser determined the range of exposure times for which this relation was valid by determining the time range over which the ratio of the lengths of two selected lines was constant. They then kept their exposure time within this range and took the relative lengths of the lines as measures of. the logarithms of their relative intensities. By this method they investigated the variation with the percentage composition of the relative intensities of homologous pairs and plotted this relationship. These curves enable one to interpolate with some degree of accuracy between the percentages fixed by equal intensities pt homologous pairs. A serious objection to this method lies in the diillculty of determining lengths of lines, for the lines do not come to an abruptend but fade out very gradually.

'schaften, p.

of a logarithmic spiral before the slit of their tain range, the length of a line produced when We have given the above resume so that the place or our contribution in thedevelopment may be better appreciated. For a more complete explanation or the prior methods reference should. be made to the following papers: Lockyear, NormanzPhiLTrans. Roy. Soc. 164 II p. 479 (1874). Hartley, W. N.: Chem. Soc. Jour. 33, p. 210, (1882). Phil. Trans. Roy. Soc. 175 II pp. 49, 325, (1884). Pollock 8: Leonard: Roy. Soc. Dublin Proc. (2) 11, pp. 217, 229, 257, e. s. (1908). De Gramont, A.: Comptes Rendus 144 p. 1101, (1906); 159, D. 6,. (1914). De Gramont 8: Boisbandrau: Analyse'Spectrale. J.Hermann, Paris (1923). Meggers, Kiess 8: Stimson: U. S. Bureau of Standards 861. Papers No. 444 vol. 18, p. 235, 120

(1922). Gerlach and Schweitzer: Die Chemische Emissions-Spektralanalyse. Leopold Voss, Leipzig, (1930). Twyman, F.: Jour. Soc. Chem. Ind. 46, pp. 284, 307, (1927). Gerlach, W. Zs. fill anorg. und allg. Chemie 142-, 389, (1925). Schweitzer, E.: Zs. fiir anorg. und allg. Chemie 164, 127, (1927),. Reis, A.: Die Naturwissen- 1114. 1926). Scheibe 8: Neuhiiusser: Zs. fiir angew. Chemie 41, 1218, (1928). Twyman 8: Simeon: Trans. Optical Sosiety'31, 169, (1930).

Our method of spectroscopic analysis is'based on the assumption that the intensity of a spectral line in the spectrum of a mixture of elements is proportional to the concentration of that element in the mixture. This assumption may be predicated upon the quantum theory of light. By the modern quantum theory of emission of light particularly by glowing gases it is generally held by physicists that light energy is emitted in definite quanta or amounts, the exact amount making up a quantum of light being related to the frequency of that particular light. These light quanta are emitted individually by individual atoms in processes characteristic of the particular atom. It is believed that the emission of light takes place coincidentally with a change in the energy state of an atomfrom one of higher to one of lower energy. In an electrical discharge such as an are or spark, atoms may be put into these higher energy states by one process or -another,--for example, by the impact of free electrons,-and are then said to be inan excited state. The concentration of atoms in any given excited state will be proportional to the concentration of atoms of that kind in the vapor of the are or spark. vapor is, of course, produced by the boiling ofi of atoms from the electrodes as aresult of heat and possibly also the application of electrical energy.

In the case of an arc, we have found that the intensity of spectral lines varies also with the arc current. We have found, however, that there is in every case a certain range of current intensities within which the variation is so slight as to be negligible and it is within this range that it is necessary to operate it thehighest accuracy is to be obtained. This discovery is an important feature ofour process.

Since we may assume that the intensity of a spectral line in the spectrum of a mixture of elements is proportional to the concentration of the corresponding element in the mixture, the obvious thing to do would be to directly measure theintensities of lines in the spectrum but no practical means has so far been developed to accomplish this. In the case, of certain inirared rays attempts have been made to measure intensities by projecting light upon a thermopile or photo-electric cell and measuring the result- [50 ing current. In the case of certain ultra-violet rays attempts have been made to measure intensities by comparing the fluorescence produced by them with the fluorescence produced by a constant standard. In these efforts it is of course obvious that the light is not measured directly but the thing that is measured is the resulting current or fluorescence. The difliculty with these methods is their uncertainty and lack of accuracy. There remains the photographic method of measurement of intensities of rays by measuring the opacities of the images producedby them on the photographic plate. As pointed out above this method cannot be used directly for there is no practical method of making in succession identical spectrograms even of the same light source because of the difllculty of controlling conditions of source, photographic technique and photographic materials. It is much less possible to control these conditions in the case of diiierent sources to a degree to make a comparison of the corresponding spectograms yield any accurate information.

In our method we make no attempt at absolute measurement of intensities nor do we attempt comparison of the spectrogram of an unknown with spectrograms of known alloys. Our method is based upon comparison of ratios of intensities of selected spectral lines in thespectrum of the unknown. It is the ratio of intensities only that we attempt to measure. Our method is based on the assumption that a given ratio of intensities of selected spectral lines in the source is peculiar to a given concentration in the source of the element producing one of the lines. The lines selected may be chosen either from the spectrum of the same element or from the spectra of different elements in the source. Thus difierent spectral lines of the same element may change in intensity at different ratesas the percentage of this element in the source varies. Therefore one can determine from the ratio of intensities of such spectral lines of an element in the alloy the percentage of that element in that kind of alloy. Since the change in the ratio of intensities of the spectral lines of a given element may be expected to be less than the change in ratio of intensities of a sensitive line of one element with respect to an insensitive line of another element, the spectroscopic analysis based upon relative intensities of two lines of a given element in an alloy would, in general, be less precise than the analysis based upon relative intensities of a sensitive line of one element and an insensitive line of another element.

In the case of nickel barium alloys we have chosen a nickel line of a wave length of 4546.9 angstrom units and a barium line of a wave length of 4554.0 angstrom units. These lines are chosen not only because the barium line is sensitive and the nickel line is insensitive, but also because they are close together in wave length. This is done because photographic plates are sensitive in difierent degrees to light of different wave lengths and by choosing lines close together in wave length this source of error is eliminated.

It will be appreciated that the accuracy of our method will depend to a considerable degree upon a proper selection of the spectral lines best fitted to give accurate indications, and this selection will vary with the elements contained in the materials to be tested and also with the range of concentrations encountered.

So far we have referred to a ratio of intensities of spectral lines in the source whereas all we are able to measure accurately is the ratio of opacities of the images of the spectral lines produced on a photographic plate. The ratio of opacities of images is not the same as the ratio of intensities so that it is necessary to evaluate opacities in terms of intensities. Other experimenters have found that the simplest relation is that err-- isting between opacities and the logarithms of intensities and while other relations between these physical quantities might be employed it is most convenient to use the simplest.

It would now seem that the obvious thing to do would be to directly measure the opacities of the spectral lines with the aid of a microphotometer and read the corresponding intensities from a standard curve showing the relation of opacities to intensities. This would lead to serious error for no two. photographic plates are alike and the slope of the opacity-intensity curve va ries not only with the condition of the emulsion on the plate but also with the wave length of the light to which it is exposed and other factors. It is therefore best to provide each plate with its own opacity-intensity curve and this may be done by the method developed by Hansen and hereinafter described. This done, the opacities of the selected lines on the plate as revealed by the microphotometer may be evaluated in terms of intensitiesyor rather in terms of logarithms of intensities, by reference to the opacity-intensity calibration curve on the same plate. The logarithm of the ratio of the intensities will be equal to the difierence in the logarithms of the intensities.

We now have a ratio of intensities of selected barium and nickel lines in the alloy and we know that this ratio is peculiar to a certain barium concentration in the alloy. To evaluate the ratio in terms of barium content it is necessary to repeat the process with a series of barium nickel alloys whose content is known by chemical analysis or by any other means. A curve may then be laid out showing the relation between the percentage of barium and the logarithms of the ratios of intensities. The ratio for the unknown may then be evaluated in terms of barium content by reference to the curve.

The method is explained in detail in connection with the accompanying drawings in which are 11- lustrated the apparatus and typical graphs employed in carrying out the method.

Fig. 1 is a typical graph showing the relation between the blackening of a lineon a photographic plate and the intensity of the light producing the line.

Figure 2 is a diagrammatic view showing one method of obtaining the spectrum and the spectographic equipment used in recording it.

Figure 3 is a reproduction of a photographic plate showing a recorded spectrum and light intensity scale.

Figure 4 is a side view and Fig. 5 is a top plan view of the apparatus employed in reproducing the light intensity scale on the photographic Figure 9 is a typical curve employed to evaluate ratios of intensities in terms of percentage of an element in the source.

Figure 10 is a typical curve showing the variation of ratio of intensities of spectral lines with changes in arc current.

Figure 11 illustrates a rotating disk sectored in the form of a'logarithmic spiral for use in front of the slit of a spectrograph.

As pointed out above it is an extremely difficult, an almost impossible task, to determine the absolute intensity of a spectral line. But it is relatively easy to measure the relative intensities of spectral lines in any given spectrum. If one has a mixture or alloy of metals in which one element is the principal constituent and another is present only in small percentages, one can reasonably assume that the presence of the lesser element will not measurably change the excitation of the spectral lines of the principal element while the lines of the lesser element will be excited to a degree proportional to its concentration in the mixture. This assumption will be most certain for such elements as do not react with one another when their atoms are excited in the electric discharge used as the spectroscopic source. If this assumption is made, it then follows that the relative intensity of a spectral line of the lesser element to that of a line of the principal element will be proportional to the concentration or percentage of the lesser element in the mixture or alloy. The results of measurement to be described later will be found to justify this assumption to a high degree of approximation. A departure from the assumed relationship may be expected when the percentage of the lesser element is sufficiently great, particularly if this element is more easily excited and ionized than the principal element as is the case with barium and nickel. This is because the lesser and more easily ionized element carries more than its proportionate share of the electric current and. furnishes more than its proportionate share of the light. Such a departure has been observed in the case of barium-nickel alloys.

The method of analysis requires first the photographing of the spectrum of the alloy and second the measuring of the relative intensities of certain lines in the photographed spectrum. The relation between the relative intensities and the percentage of one element is determined from measurements on the spectra of analyzed specimens of similar alloys for which the percentage of the element was determined by chemical analyses in some other means. Once this relation has been established any number of alloys can be analyzed without further reference to those used for calibration purposes.

We shall now describe in detail the steps in analysis of barium nickel alloys to determine the amount of barium present.

In Fig. 2 we have shown at 16 a conventional type of spectrograph equipped with a glass prism 17 and lenses 19, The spectral region recorded on the plates extended from 4200 to 4700 angstrom units. The arrangement of the auxiliary parts is shown in Figure 2. The specimen to be analyzed is cut to a size about A; inch thick, 1%, inches wide, and 1 inch long, and two such pieces, denoted by numeral 10, are then inserted in clamps, not shown, provided at the arc. The position of the clamps with respect to the spectrograph should be kept fairly constant, but it is not necessary to maintain the exact position. A screen 12 is mounted between the specimen and the spectrograph 16. This screen may be any suitable type of diffusing plate, such as a fogged photographic plate, or frosted glass. The screen serves the double purpose of diffusing the light from the are between the two specimens and of reducing the intensity of this light at the slit 18 of the spectrograph. The diffusing of the light insures that light from every point in the arc reaches the photographic plate and the reducing of the intensity enables one to increase the time of exposure of the photographic plate for a reason to be explained later.

The two specimens of the alloy to be analyzed are made the electrodes of an electric are by connecting their holders to a 220 volt D. C. power line through appropriate resistances indicated at 14. The resistances are adjusted to give a current of approximately 10 amperes through the arc.

We have found that it is important that an arc current of proper value be employed. Referring to Figure 10 it will be apparent that the relative intensities of the barium and nickel lines in the spectrum change rapidly with slight variations in the current when a current strength around 6 or 8 amperes is employed, but with current strengths around 10 amperes the change in relative intensities with slight variations in current is slight. Now it is not possible to maintain an absolutely constant arc current because of the many factors involved in producing it but the effect of fluctuations can be minimized, in this specific case, by employing an arc current in the neighborhood of ten amperes or more. In general, if the greatest accuracy is to be obtained, it will be found necessary to first work out the intensity-current curve such as indicated in Figure 10 and then choose a current in the portion of the curve where the ratio of intensities remains substantially constant.

We prefer to use a constant are rather than a spark because a spark seeks out those spots where there are low work function materials, such as barium, with the result that if the material is not distributed through the electrode homogeneously and in very minute particles or quantities the vapor will be richer in electron emitting materials than the alloy.

After the arc has run for a short time and has become steady and after some of the metal of the specimens has melted and dropped off, the photographic plate 20 in the spectrograph is exposed. Usually three exposures of 2 3, and 3 minutes duration are made and thus three spectrograms of the specimen are recorded on the plate. The spectra of four or five different specimens can be thus photographed on a single plate. The proper time of exposure for a given spectrograph and photographic plate will vary with the distance of the are from the spectrograph, with the arc current, and with the nature of the screen B.

It is important that the time of an exposure be fairly long if the material to be analyzed is not perfectly homogeneous and if an average value of the percentage of the lesser element is desired. If the material is nonhomogeneous, and particularly if the lesser element is one easily excited and ionized as is barium, a short exposure might record the spectrum at an instant when the percentage of the lesser element vaporized by the arc is considerably different from the average percentage in the material. In fact a very sensitive test of the homogeneity of the specimen can be made by making a series of short exposures and measuring the relative intensities of the spectral lines in the several spectrograms.

By this method, it was discovered that some of the barium-nickel alloys furnished for analysis were nonhomogeneous. However, if a determination of the average percentage is desired it can be obtained from measurements on spectrograms with relatively long exposure times. In two or three minutesa considerable amount of the specimen being analyzed will be melted and vaporized by a IO-ampere arc, and the relative intensities of the spectral lines recorded on the spectrogram willbe the same as the average relative intensities in the arc. When chemical analyses are made, a considerable amount of material is used and the results give the average percentage of the elements in this amount of material. Thus small inhomogeneities are not detected. The average percentage of barium in a specimen of alloy as determined spectroscopically has been found to agree closely with that determined from chemical analysis.

The kind of photographic plates used in the spectrograph has been found to be an important factor. The first plates used proved unsatisfactory because the spectral lines had different relative intensities on different plates and even in different positions on a single plate. The plates did not conform to the usual relationship between the opacity of a line on the plate and the intensity of the same line in the source. Eastman polychrome plates have been found to be free from this defect and plates of this type have been used in the analyses. It is quite likely that there are other plates on the market that may prove equally satisfactory.

In Figure 3 we have'shown a print from a specimen photographic plate 20 carrying a record made according to our process consisting of a spectrogram 21 of a sample of material and have indicated thereon nickel and barium lines that were selected for comparison of opacities and intensities of the light producing them. We also show on the plate a pattern of intensity marks now to be described. It will be understood that in our process we employ the plate or negative rather than the positive print made from the plate but for convenience in illustration we have reproduced the print in Fig. 3.

As mentioned above, there is a relationship between the opacity of a spectral line in a spectrogram recorded on a photographic plate and the intensity of the same line in the source photographed. The underlying theory of this method of analysis deals with the relative intensities of spectral lines in an arc whereas one has at hand only spectrograms on photographic plates, such spectrograms being made up of lines of different opacity or blackness. Consequently it is necessary to devise some means to determine from measurements of the relative opacities of the lines in a spectrogram the relative intensities of these lines in the arc.

As previously'explained, the relation between the blackness or opacity of a spectral line on a photographic plate and the intensity of this same line in the source is shown diagrammatically in Figure 1. Over a considerable range of opacities, i. e. from about point A on the curve to about point B, one may state the relationship by the formula.

b=A log I when b is the blackening or opacity of the line 7 on the plate, I is the intensity of the same line in the source, and A is a constant for a given plate, but varies with the type of emulsion, the

time of exposure, and the time and manner of development of the plate.

For the purpose of analysis, spectral lines of opacities lying within the range over which this formula is valid are preferred because of greater accuracy of-readings obtainable from them, but other portions of the curve may be used if preferred. Hence several exposures are made for each specimen analyzed in order to insure that one will have lines of the desired strength.

In order to evaluate the quantities involved in the formula written above another apparatus is used to record on the plate used to photograph the spectra of the materials analyzed a series of bands or stripes of varying blackness, this series of stripes being produced by light of intensity varying in a known ratio in the successive bands. Figure 3 is a reproduction of a photographic plate having recorded on it a spectrogram and one pattern of such series of bands. This method of determining the intensity scale of a photographic plate was devised by Hansen (Zeit. fiir Phys. 29, 356, 1924.). A The pattern of bands may be designated as a variable opacity calibration marker for the plate, the bands being of substantially equal area and being produced by quantities of light varying in known ratio.

Apparatus which may be used to produce the pattern from which the intensity scale of the photographic plate is determined is shown diagrammatically in Figures 4, 5 and 6. It consists of an incandescent lamp 22 whose light is made to pass through a filter 24, a diffusing screen 26,

a step-diaphragm 28, a cylindrical lens 30 and a spherical lens 32 and to fall on the photographic plate 20. This step-diaphragm 28 is shown in detail in Figure 6. It consists of an opaque screen provided with a series of openings 36. The openings are all of the same height but vary in width in logarithmic ratio, i. e., the ratio of the logarithms of the widths of successive steps is constant. Hence the total amount of light passing through the successive steps varies in logarithmic ratio. The filter 24 selects from the white light of the lamp 2. band of color, preferably blue-violet, for in this range lie the spectra to be measured. This band will be suificiently narrow so that the sensitivity of the photographic plate will be substantially the same over its whole range. Furthermore, theband will be chosen in the spectral region which includes the lines whose intensities are to be compared. The diaphragm 28 and the plate 20 are set at conjugate foci oi the spherical lens 32 and the spherical lens 32 and the diaphragm 28 are at conjugate foci of the cylindrical lens 30. This optical arrangement produces on the plate 20 bands of light corresponding to the black bands 36' Fig. 3 .in which the intensity is proportional to the widths of the corresponding steps in the diaphragm 28. Since these widths are determined from measurement, the relative intensity of the light in the several strips is known. As the intensities in successive bands are in logarithmic ratio, the blackening of the plate in successive strips will have a linear variation, according to the law b=A log I over a certain range of intensities.

The blackening or opacity of the photographic plate may be measured by means of a self-recording microphotometer. A number of kinds suitable for this work are now available. The one used in this investigation was made by Kipp and Son of Delft, Holland. This instrument is illustrated diagrammatically in Figure 7. The straight-line filament 38 of a tungsten lamp is focused by means of lens on a narrow slit 42 and a very small, sharp image of this slit is formed by means of lens 44 on the emulsion of the photographic plate 20 bearing the spectrograms and intensity marks. Some of the light is absorbed by the silver in the emulsion of the photographic plate and the balance is passed through another lens 46 and focused on the junctions of a thermopile 48. The heating of the thermopile by the light falling on it generates an E. M. F. which causes a proportional current to pass through the galvanometer 50 and produces there a corresponding deflection. A beam of light from a suitable source 52 is reflected by the galvanometer mirror 54 and is focused onto a strip of high speed sensitized paper 56 fastened on a drum 58. The amount of light passing to the thermopile 48 will be reduced when a spectral line of the plate is drawn into the light beam by an amount which varies with the opacity of the line. The corresponding change in current through the galvanometer 50 produces a proportional deflection of the light beam on the drum 58. The plate 20 is carried through the light beam and the drum 58 is simultaneously rotated by appropriate gearing 60 operated by a small motor 62. Thus the deflections of the light beam on the drum 58 which measure the relative opacities of the spectral lines on the plate 20 are automatically recorded. In the same manner the relative opacities of the intensity calibration bands are recorded on the same sensitized paper. A specimen record is reproduced in Figure 8.

The record reproduced in Figure 8 shows the galvanometer deflections corresponding to the opacities of the two chosen spectral lines, 4554.0

, A. of barium and 4546.9 A. of nickel, on the plate 20 from which Fig. 3 was obtained. At the left in the figure is the record of the relative opacities of the successive stripes in the pattern of intensity marks on the same plate. The opacity increases with the distance from the zero line at the bottom of the figure. For convenience the heights of the successive steps are measured and plotted against the logarithms of the intensities of the light producing the successive stripes as shown in Figure 1. It will be remembered that the intensities of the light in the several bands of the intensity pattern varied in a logarithmic ratio because the stepped openings in the diaphragm 28 were made with areas in that ratio, and the amount of light passing through the openings varied in' the same ratio because of uniformity of illumination of the d.'ffusing screen 26 constituting the source. The ordinates are propor-- tional to the opacities of the successive strips. The curve has a straight line portion in which the law b=A log I is valid. From this curve the logarithms of the relative intensities of the barium and nickel lines on this same plate can be determined by applying to it the measured opacities of these lines. That is, the height of the peak in the opacity curve of Fig. 8 corresponding to the barium line is measured and laid off as an ordinate on Fig. 1. The corresponding abscissa (5.7) is proportional to the logarithm of the intensity of the light producing the barium line. The same thing is done with the peak in the opacity curve of Fig. 8 corresponding to the nickel line, and the abscissa (3.8) is obtained which is pro portional to the logarithm of the intensity of the light producing the nickel line. The logarithm of the ratio of the intensity of the barium line to that of the nickel line,

in the spectrum of the alloy can now be found by subtracting the logarithm of the intensity of the latter from that of the former: (5.7)-(3.8)=

It is now necessary to evaluate the last named logarithm in terms of barium or nickel content and this is done as follows:

The values of log K were determined for a number of alloys that had been analyzed chemically and when these values were plotted against the percentage of barium in these alloys the curve reproduced in Figure 9 resulted.

We now apply log 7;

of the unknown, which we have found to be (1.9), to the curve, Fig. 9, and find the corresponding barium content to be (.155)%. We have been able to repeatedly check the results thus obtained against chemical analyses and find no error. When on one occasion the spectroscopic analysis did not agree with the chemical analysis, a reexamination of the chemical analysis revealed an error in calculation, which when corrected pro duced conformity in analyses.

This curve, Fig. 9, has been used in the spectroscopic determination of all subsequent nickelbarium alloys. As will be observed from the ordinate scale, the curve can be read to .001% Ba. Tests show that repeated measurements agree with .005% Ba unless the alloy is grossly inhomogeneous.

In general, our method of quantitative spectrographic analysis consists of the following steps:

I. The fixing of the excitation conditions.

An arc between electrodes consisting of or containing the material to be tested is used and the relation between the relative intensity of selected spectral lines and the arc current, as indicated 8. g. in Figure 4, is determined. A value of arc current is chosen at which, for a small change in current, the change in relative intensity of the lines is small. A spark source may be used and standardized by the method of Gerlach and Schweitzer.

II. The determining of the working curve.

A series of alloys, solutions, or mixtures is made in which the percentage composition of the material to be estimated is varied over the range chosen for the analysis. The value of the logarithm of the relative intensites of the selected lines is determined for each alloy in the series. In every case the spectrum is excited in the manner indicated by the experiments under I. Usually an arc source is used. These results are plotted as in Figure 9.

III. The analysis of an unknown specimen.

The spectrum of the unknown specimen is photographed in the manner determined under I and the logarithm of the relative intensities of the selected lines is determined as follows: The opacities of the selected lines are measured by a suitable densitometer or microphotometer. These values of the opacites are applied to a scale as indicated in Figure 1 and the logarithm of the Y mind just what is meant relative intensities of the lines is obtained by subtracting the value (indicated by the scale) of the'logarithm of the intensity of one of the lines from that of the other line. A scale like that in Figure 1 is determined for each photographic plate by measuring the opacities of a set of stripes or bands photographed on the plate by the use of a calibrated step diagraph. The logarithm of the relative intensities of the spectral lines is applied to the working curve, Figure 6, and the percentage composition is read on the scale.

- One working curve suffices for a considerable range of percentage compositions of a given kind of material." Steps I and II need be performed but once for a particular kind of alloy, solution,

or mixture. Step III alone must be repeated for each analysis. In this step, only onecalibration curve, Figure 1, is necessary for a plate which may bear the spectrograms of a number, ten or twelve, of specimens to be analyzed. In the cases of Ba-Ni and Cr-Ni alloys, the spectrographic analyses have been found to be as accurate as chemical analyses and can be carried out in a small fraction of the time required for chemical analyses.

In the foregoing discussion the intensity of a spectral line has been carefully differentiated from the strength or blackness or opacity of a line on a photographic plate. In much of the literature to which reference has been made, these terms have not been differentiated and the term intensity has been applied to the strength of a spectral line. It is essential that one keep in by the terms as used by the several writers because one can readily show that the intensity (as used in this paper) of a spectral line is related to the concentration in the source of the element giving rise to it, while no simple relationship exists between the strength of a line and the concentration of an element in the source.

The entire process requires approximately two hours to complete. The process time may be shortened to 15 to 20 minutes by employing a microphotometer with a visual indicator instead of a recorder. The developing, fixing and drying of the opacity record is thereby eliminated.

Our preferred method has a number, of important advantages. It gives a complete calibration curve for the plate carrying the spectrograms and thus one knows when the relation b=A log I is valid; and one is not limited to the range of intensities for which this relationship holds. Furthermore, as pointed out before, it is diiiicult to determineexactly the length of a spectral line produced with a sectored disk because such lines do not end abruptly but gradually fade out. However, the rotating sector method eliminates the necessity of a microphotometer or densitometer and may be accurate enough for some purposes.

The recent workby others which has shown the most promise has been largely confined to the study of spark spectra. By our method of quantitative analysis we have found it possible to make accurate analyses by the use of an arc source as well as a spark source. The are has the advantage over the spark in that the spectral lines, especially are lines, are much more uniform over the length of the arc. Furthermore the arc consumes more material of the electrodes than does a spark and hence gives a better average composition. A spark will seek out points on the are strikes to a considerable fraction of the surface of the ends of the electrodes.

The are and spark spectra of many common heavy metals, as iron, nickel, tungsten, molybdenum, etc, contain a great many spectral lines. In analyzing for these elements or for other elements in alloys containing them, one must use a spectrograph of considerable resolving power in order to separate the lines used inthe analysis from neighboring lines, sufficiently to make possible an accurate measure of their densities. For high resolution, a Littrow mounting quartz spectrograph has been found convenient. This type of spectrograph gives a maximum resolution for a given size (length) of instrument. It has the disadvantage, however, in that a certain amount of light is reflected from the lens onto the photographic plate and produces some plate fog. The amount of fog becomes sufficient to cause serious difficulty in the determination of line intensities when one uses lines near the ultraviolet limit of the range of the spectrograph. For example, we experienced considerable difliculty in measuring the relative intensities of lines in the neighborhood of 2500 A. The fog was completely eliminated and the difflculty completely overcome by placing a quartz cell containing chlorine gas at a pressure of about five and a' half atmospheres before the slit of the spectrograph. Such a cell transmits light at 2500 A. but absorbs practically all light in the range from 2550 to 4800 A.

It will be apparent that our process may be carried out with the use of a sectored disk in the manner set forth by Scheibe and Neuhausser. In this case the first step, that of ascertaining the proper value of arc current, would be the same as in the preferred method. In the second and third steps the photographs of the spectra would be taken in the manner described by Scheibe and Neuhausser, but instead of calculating and plotting ratios of intensities of spectral lines, ratios of lengths of lines would be calculated, plotted and read off the calibration curves in the same manner as in our preferred method. It will be remembered that by using a sectored disk the ratio of lengths of lines becomes roughly a measure of ratio of logarithms of intensities. By employing this method simplification is obtained at the expense of accuracy. Spectroscopic methods of analysis are necessarily limited to ascertainment of percentages of elements since it is the element only that produced spectral lines, but we believe it is applicable to all elements and in whatever combination they occur except in cases where their char-. acteristic lines are not revealed in the spectrum. Thus our method could not be used to determine the amounts of nitrogen, oxygen, fluorine, chlorine, iodine or bromine in combination with metallic elements for their spectral lines are not then visible. However, in such cases it would be possible to ascertain the amount of the metallic element and from this it mightbe possible to calculate the percentage of the element whose spectral line is not revealed. In all other cases our method is directly applicable, whether the materials be in solid, liquid, gaseous or any other form.

It must be obvious also that our fundamental conception of measuring amounts of elements by comparison of ratios of intensities of spectral lines is not limited to the specific method of measuring intensities herein disclosed. It is equally applicable whatever method be used to to eliminate many sources of error.

In case of certain alloys or mixtures which may be very diflicult of chemical analysis and where no great accuracy is required, it may be sufllcient to measure the intensity of a spectral line by our photographic method and evaluate the measurement in terms of data compiled from like tests of specimens of known chemical content. Eliminating the comparison of ratios very greatly reduces the accuracy of the method because of the practical impossibility of repeating the same conditions of source and photography but the use of the intensity marks on the plate removes inaccuracies resulting from non-uniformity of plates and from different treatment oi difl'erent plates after exposure and, more than this, from the errors which have heretofore crept in because of use of ratios of opacities instead of ratios of intensities.

It is of course apparent that our method requires special curve showing the relation between percentages of an element in the specimen and the ration of intensities of spectral lines for each class of specimen, and this in turn requires careful preparation of specimens of known chemical content. However this need be done but once and thereafter any number of analyses may be made spectroscopically from this data. Repetition of tedious quantitative chemical analyses upon diflerent batches of the same kind of material is thus a'voided.

Adaptation of our method to industry will unquestionably result in improvement in the neces sary apparatus to increase the speed of analysis and reduce the cost of equipment. With this object in view it may be desirable to so design the spectrograph that the intensity pattern may be applied at the same time that the photograph of the spectrum is made. Thugthe times of ex- .posure of the two could be mechanically correlated so that it might not be necessary to take more than one exposure to bring the opacities of the spectral lines to be studied at a portion of the opacity-intensity curve where an accurate reading may be obtained.

If preferred the plates could be marked in advance with the light intensity scale, ready for use in the spectrograph, but this will affect the reliability of the readings because of change in the plates with passage of time.

The exposed and developed photographic plates made according to our process may be measured in the microphotometer while still wet for the thin film of water has little effect on the light beam and that effect is substantially uniform across the plate.

The microphotometer may be of any desired type as pointed out previously and instead of recording on a photographic roll may be provided with a dial and pointer or the like to indicate opacities, or may reproduce opacities in the form of a curve traced by a beam of light on a frosted glass screen. Many modifications will occur to skilled instrument makers.

While we have used the term opacity to define the characteristic of the spectral lines that we measure, it is to be understood that we have not used the term in an exact technical sense, but merely to indicate a quality of the line, whether that quality be technically opacity, density, or blackening.

We claim:

1. The method of quantitative spectroscopic analysis which comprises the following steps:

establishing an arc cin'rent between electrodes comprising the unknown material of a value such that the intensity of spectral lines does not vary materially with unavoidable fluctuations in arc current, recording the spectrum of the arc, measuring the ratio of intensities of a pair of lines in the spectrum by comparison of the strengths of the corresponding recorded lines, repeating the process with a series of electrodescontaining the same kind of material but of known analysis, making use' of the same spectral lines, evaluating the ratio of intensities obtained from the unknown material in terms of percentage of an element producing one of the lines by comparing the ratio of intensity of the unknown with the ratio of intensity of said known specimens.

2. The method of quantitative spectroscopic analysis which comprises the following steps; establishing a luminous discharge between electrodes comprising the unknown material, recording the spectrum thereof on a Photographic plate, recording on the same plate a series of marks produced by light of intensity varying in known ratio, measuring the opacity of'a pair of spectral lines on the plate in terms of the opacities of 1 said marks; evaluating said opacity measurements in terms of the intensities producing the marks and obtaining therefrom a ratio of intensities of said spectral lines, repeating the process with a series of electrodes containing the same kind 1 of material but of known analysis making use of the same spectral lines, evaluating the ratio of intensities obtained from the unknown material in terms of percentage of an element producing one of the lines by comparing the ratio 1 of intensity of the unknown with the ratios of intensities of the said known specimens.

3. The method of quantitative spectroscopic analysis which comprises the following steps: establishing an arc current between electrodes comprising the unknown material of a value such that the intensity of spectral lines does not vary materially with unavoidable fluctuations in arc current, recording the spectrum of the are on a photographic plate, recording on the same plate 11 a series of marks produced by light of intensity varying in known ratio, measuring the opacity of a pair of spectral lines on the plate in terms of the opacities of said marks, evaluating said opacity measurements in terms of the intensities l1 producing the marks and obtaining therefrom a ratio of intensities of said spectral lines, repeating the process with a series of electrodes containing the same kind of material but of known analysis making use of the same spectral lines, 12

evaluating the ratio of intensities obtained from the unknown material in terms of percentage of an element producing one of the lines by comparing the ratio of intensity of the unknown with the ratios of intensities of the said known speci- 1:

mens.

4. The method of quantitative spectroscopic analysis comprising recording at least a portion of the spectrum of a specimen of unknown analysis on a photographic plate, recording on the 14 of said marks, measuring the opacity of another 14 spectral line produced on the plate by the specimen in terms of the opacities of said marks, evaluating said opacity measurements interms of the intensities producing the marks, evaluating the ratio of intensities thus ascertained in 15 terms of amounts of an element in the specimen producing at least one of the lines by reference to data compiled from like tests of specimens of known composition.

5. The method of quantitative spectroscopic analysis comprising recording at least a portion of the spectrum of a specimen of unknown analysis on a photographic plate, recording on the same plate a series of marks produced by light from approximately the same portion of the spectrum and of intensity varying in known degree, measuring the opacity of a. selected spectral line produced on the plate by the specimen in terms of the opacities of said marks, measuring the opacity of another selected spectral line produced on the plate by the specimen in terms of the opacities of said marks, evaluating said opacity measurements in terms of the intensities producing the marks, evaluating the ratio of intensities thus ascertained in terms of amounts of an element in the specimen producing at least one of the lines by reference to data compiled from like tests of specimens of known composition.

6. The method of quantitative spectroscopic analysis comprising recording at least a portion of the spectrum of a specimen of unknown analysis on a photographic plate, recording on the same plate a series of marks produced by light of intensity varying in known ratio, measuring the opacity of a selected spectral line produced on the plate by one element of the specimen in terms of the opacities of said marks, measuring the opacity of a selected spectral line produced on the plate by another element of the speci men in terms of the opacities of said marks, evaluating said opacity measurements in terms of the intensities producing the marks, evaluating the ratio of intensities thus ascertained in terms of amounts'of one of the said elements in the specimen by reference to data compiled from like tests of specimens of knowncomposition.

7. A method of quantitative spectroscopic analysis comprising recording at. least a portion of the spectrum of a specimen of unknown analysis on a photographic plate, recording on the same plate a series of marks produced by light of intensity varying in known degree, measuring the opacity of a selected spectral line produced on the plate by one element of the specimen in terms of the opacities of said marks, evaluating said opacity measurement in terms of the known intensity producing the mark, evaluating the intensity thus ascertained in terms of amounts of the elements in the specimen by reference to data compiled from like tests of specimens of known composition.

8. ,The method of quantitative spectroscopic analysis comprising recording at least a portion of the spectrum of, a specimen of unknown analysis on a photographic plate, recording on 'the same plate a series of marks produced by light from approximately the same portion of the spectrum of intensity varying in known ratio, exposing the plate in a microphotometer or densitometer and securing indications of the opacities of selected lines produced on the plate,

and indications of the opacities of the said series of marks, evaluating the indications of amounts of one of the said elements in the specimen by reference to data compiled from like tests of specimens of known composition.

9. The method of quantitative spectroscopic analysis which comprises the following steps: causing the material to emit light; recording on a photograph plate the spectrum -,thereof together with a variable opacity calibration marker; comparing the opacities of a recorded pair of lines with the opacities of said marker to obtain the ratio of quantities of light producing the corresponding spectral lines; repeating the process with a series of electrodes containing the same kind of material but having the substance correspondirig to one'of said spectral lines varied in known amount; repeating the process with a specimen of unknown analysis; evaluating the ratio of light quantities obtained from the unknown material in terms of percentage of said substance by comparison with the ratios of light quantities previously obtained.

10. The method of quantitative spectroscopic analysis which comprises the following steps: establishing an electric discharge, as an are or spark, between electrodes comprising the material to be analyzed, recording the spectrum thereof on a photographic plate, recording on the same plate a series of marks produced by quantities oflight varying in known ratio, comparing the opacities of a pair of spectral lines on the plate with the opacities of said marks and thereby evaluating the opacity measurements of said lines interms of the quantities of light producing the marks, repeating the process with a series of electrodes containing the same kind of material but having the substance corresponding to one of the lines varied in known amount; repeating the process with a specimen of unknown analysis, evaluating the ratio of light quantities obtained from the unknown material in terms of percentage of said substance by comparing the ratio of light quantities of the unknown with the ratios of light quantities of the said known specimens.

11. The method of quantitative spectroscopic analysis comprising recording at least a portion of the spectrum of a specimen of unknown analysis on a photographic plate,. recording on the same plate a series of marks of varied opacity produced by quantities of lightvarying in known ratio, measuring the opacity of a spectral line produced on the plate by the specimen in terms of the opacities of said marks, masuring the opacity of another spectral line produced on the plate by the specimen interms of the opacities of said marks, evaluating said opacity measurements in terms of'the quantities of light producing the marks evaluating the ratio of quana tion.

ORA S. DUFFENDACK. RALPH A. WOLFE. 

